1. Field of the Invention
The present invention relates to electronic instruments for testing optical devices, and in particular to a method and apparatus for measuring polarization mode dispersion (PMD) of a dispersion grating, such as a dispersion compensation grating (DCG).
2. Description of the Related Art
As a light pulse, with a finite spectrum of optical frequencies, travels through a medium, e.g., an optical fiber, two dispersion phenomena occur. First, because light travels through the medium at different velocities depending on its frequency, the pulse of multiple frequency will experience a chromatic dispersion and will be spread out in time during its propagation through the medium. Second, a polarization mode dispersion (PMD) occurs because light travels through the medium at different velocities depending on its polarization. It is well known that PMD can limit the available transmission bandwidth in fiber optics transmission links. In other words, as the bit rate of a system increases, the PMD tolerance of that system decreases.
To minimize the chromatic dispersion in high bit rate systems (for example, a OC-48 system having a 2.488 Gbps bit rate) it has been suggested to connect the optical fiber to a dispersion compensation grating (DCG). Such DCG is specifically designed to compensate for chromatic dispersion. However, a DCG may potentially increase PMD in the optical fiber/DCG system, and thus, may deteriorate transmission in high bit rate systems. There is, therefore, a need for a method and apparatus capable of accurately measuring PMD of a DCG so as to determine whether a particular DCG can be incorporated into a high bit rate optical fiber system without deterioration of the optical signal.
Several conventional methods exist to measure PMD in optical fibers. In particular, a well-established method for measuring PMD in optical fibers uses the so-called "Jones Matrix Eigenanalysis" (JME). A description of this method is provided for example in U.S. Pat. Nos. 5,227,623 and 5,298,972 to Hefner and in B. L. Hefflier, "Automated Measurement of Polarization Mode Dispersion Using Jones Matrix Eigenanalysis", IEEE Photonics Technology Letters, Vol. 4, No. 9, September 1992, the entire contents of which are hereby incorporated by reference.
An example of an apparatus used in the conventional JME method to measure PMD in an optical fiber is shown in FIG. 1. An optical source 10, which may be a conventional tunable laser source, generates sequential optical beams with different frequencies/wavelengths, for example 1300 nm and 1302 nm. The polarization synthesizer 20 receives the optical beams from the optical source 10 and produces three sequential states of polarization for each optical beam. Preferably, the three states of polarization are separated by 60.degree.. The polarized optical beams travel sequentially though the optical fiber 30 under test, which produces the PMD being measured. The optical beams, having experienced PMD through the optical fiber, then enter an analyzer 40, such as an optical polarization meter. Optical polarization meter 40 measures the intensity of the received optical beams with the different polarizations and generates the so called "Stokes parameters," which are well known in the art and defined in Principles of Optics, by M. Born and E. Wolf, Pergamon Press, 4.sup.th Edition, London, 1970, pages 30-32, the content of which is hereby incorporated by reference. For each optical beam with a particular wavelength, the Jones matrices are then computed in processor 50 from the measured responses, i.e., from the Stokes parameters, according to a known algorithm. One such algorithm is described in U.S. Pat. No. 5,298,972, the entire content of which is hereby incorporated by reference.
Processor 50 may be a conventional personal computer and can be connected to the optical source 10 to read and set the frequency of the optical beams. Processor 50 is also connected to polarization synthesizer 20 to read and set the polarization of the optical beams. Once the Jones matrices, which capture the characteristics of the optical fiber under test, are determined, then PMD can be determined using a conventional Jones Matrix Eigenanalysis, which is well known to persons of ordinary skill in the art, described for example in U.S. Pat. No. 5,227,623 at column 12, line 21 to column 16, line 21, the entire content of which is incorporated herewith by reference.
Briefly summarizing, the conventional Jones Matrix Eigenanalysis method for measuring PMD in an optical fiber, defines the following quantities:
E.sub.1 (.omega.) is the input field of an optical beam of frequency .omega. before entering an optical fiber. E.sub.1 (.omega.) has a unit vector e.sub.1. PA1 E.sub.2 (.omega.) is the output field of an optical beam of frequency .omega. after exiting the optical fiber. E.sub.2 (.omega.) has a unit vector e.sub.2. PA1 T(.omega.) is the Jones matrix, characteristic of the optical fiber, so that EQU E.sub.2 (.omega.)=T(.omega.).multidot.e.sub.1. (1)
The output field E.sub.2 (.omega.) can be expressed in terms of a magnitude term .sigma.(.omega.) and a phase conponent .phi.(.omega.): EQU E.sub.2 (.omega.)=.sigma.(.omega.) e.sup.i.phi.(.omega.) e.sub.2. (2)
Taking the partial derivative of E.sub.2 (.omega.) with respect to .omega., and using the prime symbol to denote differentiation with respect to .omega., one obtains: EQU E'.sub.2 (.omega.)=T'(.omega.).multidot.e.sub.1 =(.sigma.'(.omega.)/.sigma.(.omega.)+i.phi.'(.omega.))E.sub.2 (.omega.), (3)
where .delta.e.sub.1 /.delta..omega.=0 because e.sub.1 is fixed at input and .delta.e.sub.2 /.delta..omega. is 0 to first order over .omega.. From Equation (1) and assuming that the optical fiber is not perfectly polarizing so that its Jones matrix is non-singular, one obtains: EQU e.sub.1 =T.sup.-1 (.omega.).multidot.E.sub.2 (.omega.). (4)
Inserting (4) into (3) and using the approximation T'(.omega.)=[T(.omega.+.DELTA..omega.)-T(.omega.)]/.DELTA..omega., one obtains: EQU [T(.omega.+.DELTA..omega.)-T(.omega.)]/.DELTA..omega..multidot.T.sup.-1 (.omega.).multidot.E.sub.2 (.omega.)=(.sigma.'(.omega.)/.sigma.(.omega.)+i.phi.'(.omega.))E.sub.2 (.omega.), which simplifies
to: EQU T(.omega.+.DELTA..omega.).multidot.T.sup.-1 (.omega.)-(1+i.phi.'(.omega.).DELTA..omega.)I=0, (5)
where I is the unit matrix, and where it is assumed that .DELTA..omega..multidot..sigma.'(.omega.)/.sigma.(.omega.) is 0 for small .DELTA..omega. because losses are essentially the same at .omega. and at .omega.+.DELTA..omega..
For an optical fiber, it is assumed that the phase component of the output field, .phi.(.omega.), is the product of a propagation constant, .beta. which is a function of frequency, times the distance z traveled by the light beam along the axis of the optical fiber. For an optical fiber, it is assumed that z is independent of frequency, so that: EQU .phi.(.omega.)=.beta.(.omega.).multidot.z, and .phi.'(.omega.)=.delta..beta.(.omega.)/.delta..omega..multidot.z.
.delta..beta.(.omega.)/.delta.(.omega.) is the reciprocal of the group velocity v.sub.g, so that EQU .phi.'(.omega.)=z/v.sub.g =.tau..sub.g, (6)
where .tau..sub.g is the group delay of the optical beam through the optical fiber. Substituting (6) into (5) and solving (5) for the eigenvalues gives: EQU .DELTA..tau.=.tau..sub.g,I -.tau..sub.g,II =Arg(.rho..sub.I /.rho..sub.II)/.DELTA..omega., (7)
where I and II denote the two principal states of polarization; .rho..sub.I and .rho..sub.II are the eigenvalues of T(.omega.+.DELTA..omega.).multidot.T.sup.-1 (.omega.); Arg denotes the argument function; and .DELTA..tau., which is called the differential group delay, corresponds to the PMD in the optical fiber. The computation of .DELTA..tau. is performed by processor 50, which is configured to carry out the above analysis based on the data received from optical polarization meter 40.
As noted above, the conventional JME method asssumes that the length of the traveled optical path by light, z, is independent of frequency, so that AT corresponds exclusively to the effect of PMD. This is an accurate assumption in optical fibers, and JME is thus an accurate method for measuring PMD in optical fibers.
However, in a DCG, by definition, the length of the optical path traveled by light, z, is dependent of frequency, i.e., z=z(.omega.). Specifically, light is reflected off a DCG at a depth that is dependent of its frequency. The DCG is designed so that the difference in travel time for different wavelengths caused by the difference in length of the optical path traveled by the light of different wavelength offsets, or compensates for, the difference in traveled time caused by the chromatic dispersion. Consequently, in a DCG, light of different wavelengths will have different lengths of traveled optical path and the JME assumption noted above is no longer correct. Thus, if the conventional JME method were to be used to measure PMD of a DCG, the computed differential group delay, .DELTA..tau., would not correspond to the true PMD of the DCG, but to the sum of the delay caused by PMD plus any delay caused by the difference in length of the traveled optical path in the DCG. Therefore, using the conventional JME method for measuring PMD in a DCG does not give an accurate result.